The questionable part is under class App extends React.Component. I am trying to re-render the Leader Component with the state change in the update method. it changes states, but then does not change the property passed to Leader to rerender.

You're not doing anything inside Leader with the prop m after it's initial render. So, it is re-rendering, but its state hasn't changed. Remember that the constructor is only called once, before the initial render. So, if you want Leader to respond to prop changes after the initial render and update its state accordingly, you need to use one of the component lifecycle methods.